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number theory

by PAB2706 » Sat Aug 27, 2011 10:27 pm
If T is a set of more than two numbers, is
the sum of all the elements in set T equal
to zero?
(1) If n is in T, then -n is also in T.
(2) The number of negative numbers in
T equals the number of positive numbers
in T.
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Source: — Data Sufficiency |
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by Frankenstein » Sat Aug 27, 2011 10:57 pm
Hi,
The question doesn't say distinct elements, so we can consider repetitions:
Consider the set, T = {2,4,4,-2,-2,-4} -> sum of elements is not equal to zero.
Consider the set, T = {2,4,6,-2,-4,-6} -> sum of elements is equal to zero.

Hence E

OA please?
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by jonathan123456 » Sun Aug 28, 2011 3:01 am
IMO E
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by apex231 » Sun Aug 28, 2011 9:01 am
(1) If n is in T, then -n is also in T. - Numbers may repeat. Not sufficient.

(2) The number of negative numbers in T equals the number of positive numbers
in T. - No information on what numbers set contains. Not sufficient.


stmt 1 and 2 together - We know for every n there is -n and number of positive numbers is equal to number of negative numbers.

Hence, Sufficient.
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by prateek_guy2004 » Sun Aug 28, 2011 2:27 pm
(1) If n is in T, then -n is also in T. Not suff
(2) The number of negative numbers in Not suff

We can not conclude both statements...

E
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by force5 » Sun Aug 28, 2011 2:37 pm
Yes Answer shld be E
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by apex231 » Sun Aug 28, 2011 3:41 pm
Can someone explain why stmt 1 and stmt 2 together are not sufficient? I think together they are sufficient to answer.

Please post explanations along with the answers.
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by czarczar » Sun Aug 28, 2011 5:06 pm
IMO :E

Can be -2,-4 ,-2 and 2,4,2 or -2,-4,-2 and 2,4,4.
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by GmatKiss » Sun Aug 28, 2011 11:52 pm
IMO:E
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by saketk » Mon Aug 29, 2011 4:05 am
Frankenstein wrote:Hi,
The question doesn't say distinct elements, so we can consider repetitions:
Consider the set, T = {2,4,4,-2,-2,-4} -> sum of elements is not equal to zero.
Consider the set, T = {2,4,6,-2,-4,-6} -> sum of elements is equal to zero.

Hence E

OA please?
HI Frankenstein -- If we consider the second statement then the case of repetition can be eliminated..

total positives = total negatives

I think answer should be C ( BOTH STATEMENT TOGETHER ARE SUFFICIENT)
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by Frankenstein » Mon Aug 29, 2011 4:31 am
saketk wrote:
Frankenstein wrote:Hi,
The question doesn't say distinct elements, so we can consider repetitions:
Consider the set, T = {2,4,4,-2,-2,-4} -> sum of elements is not equal to zero.
Consider the set, T = {2,4,6,-2,-4,-6} -> sum of elements is equal to zero.

Hence E

OA please?
HI Frankenstein -- If we consider the second statement then the case of repetition can be eliminated..

total positives = total negatives

I think answer should be C ( BOTH STATEMENT TOGETHER ARE SUFFICIENT)
Hi,

The examples I have used satisfy both the conditions. Still we can't say that the sum of elements is zero. I don't understand how repetition is eliminated by 2nd statement.
{2,4,4,-2,-2,-4} and {2,4,6,-2,-4,-6} both satisfy statement (2). Still not enough to say whether sum is zero or not.
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by navami » Mon Aug 29, 2011 7:51 am
Great goin guys ... u ve explained it really well .
I too think it will be E
This time no looking back!!!
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by saketk » Mon Aug 29, 2011 11:25 pm
Frankenstein wrote:
saketk wrote:
Frankenstein wrote:Hi,
The question doesn't say distinct elements, so we can consider repetitions:
Consider the set, T = {2,4,4,-2,-2,-4} -> sum of elements is not equal to zero.
Consider the set, T = {2,4,6,-2,-4,-6} -> sum of elements is equal to zero.

Hence E

OA please?
HI Frankenstein -- If we consider the second statement then the case of repetition can be eliminated..

total positives = total negatives

I think answer should be C ( BOTH STATEMENT TOGETHER ARE SUFFICIENT)
Hi,

The examples I have used satisfy both the conditions. Still we can't say that the sum of elements is zero. I don't understand how repetition is eliminated by 2nd statement.
{2,4,4,-2,-2,-4} and {2,4,6,-2,-4,-6} both satisfy statement (2). Still not enough to say whether sum is zero or not.
yeah got it -- {5,-5,-5,6,6,-6} is an example -- Hence E is the answer.
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